A349613 Dirichlet convolution of A064413 (EKG-permutation) with the Dirichlet inverse of its inverse permutation.

1, 0, -1, 3, -7, 7, -2, -6, 9, 10, -5, -15, -14, -2, 55, 10, -17, -41, -15, -36, 42, 18, -13, 44, 81, 29, -35, -45, -18, -180, -29, -23, 41, 53, 135, 99, -48, 51, 114, 131, -30, -140, -58, -53, -303, 34, -37, -120, 34, -196, 147, -87, -45, 226, 207, 166, 103, 67, -41, 466, -84, 91, -288, 13, 350, -258, -91, -108

Offset

1,4

Comments

Obviously, convolving this with A064664 gives A064413 back.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to EKG sequence

Formula

a(n) = Sum_{d|n} A064413(d) * A323411(n/d).

Prog

(PARI)
up_to = 32768;
v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ Data prepared with Chai Wah Wu's Dec 08 2014 Python-program given in A064413.
A064413(n) = v064413[n];
\\ Then its inverse A064664 is prepared:
m064664 = Map();
for(n=1, 65539, mapput(m064664, A064413(n), n));
A064664(n) = mapget(m064664, n);
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
v323411 = DirInverseCorrect(vector(up_to, n, A064664(n)));
A323411(n) = v323411[n];
A349613(n) = sumdiv(n, d, A064413(d)*A323411(n/d));

Crossrefs

Cf. A064413, A064664, A323411, A349614 (Dirichlet inverse), A349615 (sum with it), A349616.

Cf. also pairs A349376, A349377 and A349397, A349398 for similar constructions.

Sequence in context: A131707 A348722 A349614 * A016620 A200691 A021269

Adjacent sequences: A349610 A349611 A349612 * A349614 A349615 A349616

Keyword

sign

Author

Antti Karttunen, Nov 23 2021

Status

approved